Radicals have names, they don’t have reading. A square has a name, not a reading of it.

But furthermore, there is one 部首 in a Kanji. You can not explain how to write Kanji with radicals because in 掴む only 手偏 is a radical, which does not have a way of reading, it simply has a name. You would simply say 左、手偏。右,「クノ」の漢字を書いて。You can’t “read” the hand radical any other way because it has no phonetic information encoded in it. 手偏 is also a straightforward example, but many are not.

If you needed to explain any further, you would use 永字八法 followed by words such as 跳ね

The difference between 読み方 for names is that you are looking at Kanji and they have a way to be read in Kana with their pronunciations. You’re asking them because you don’t know which readings to use. To go back to the beginning, radicals don’t have these because they only have names.

All names are readings. By definition, a reading is an oral interpretation of written language. The reading of "square is /skwɛɚ/ in America, as IPA is the English form of radicals. And yes, all IPA characters have names with have readings in order to understand how to pronounce those names. You can indeed “read” the hand radical. For example, if we were talking in person, you just “read” the radical by using the term “hand radical.”

I’ll use it to explain my stance as well to be consistent.

First, using 左 to explain 手偏 is completely redundant, as the name itself already indicates it will be on the left. That is the phonetic information that 手偏 provides. You’re effectively telling someone to write the left side on the left.

Second, you say 手偏 doesn’t have a way of reading, but that name is made of of kanji. You yourself also just claimed that 読み方 are for kanji. What’s stopping me from pronouncing it 「しゅへん」? 手偏 is a 熟語, so there should be nothing wrong with a beginner assuming they’d use the 音読み. Furthermore, 手偏 uses the 訓読み of 手 and the 音読み of 偏. That’s not straightforward at all. I was intentionally using 平仮名 because I personally see radicals named more often in it than in 漢字, so you’re actually helping me argument even more by providing the names in 漢字, which you yourself just claimed have 読み方. What makes 手偏 different from 手紙、相手、助手、or any other kanji with 手.

Third, your claim that 漢字 only have one 部首 is only correct by a technical standpoint. Your example also requires that someone know the 漢字 for 国, which, if they don’t, requires explaining that you have 玉 inside of くにがまえ. Now you have two 部首 to explain. For every 漢字 containing a 部首 and component (as opposed to being both, such as 木 and 玉), you have to break down the 漢字 further, and for every 漢字 you explain, you have an additional 部首.

鬱 for example has 缶, 木、and 鬯、all of which should be understood by meaning (as they are both kanji and radicals). On the other hand, 彡, 冖, 匕, and 凵 would all be quite annoying to explain if you don’t know their names. Sure you could do it the hard way with stroke names and counts, or you could simplify the process by just using names that already contain that information.